I've run over it a lot, and I've come to the same conclusion as Jake, it's not worth it to upgrade the whole thing. I've instead decided that I'll get:
New chain
Shifters: best left I can find (since they're all 3 speed) and a 7 speed right (preferably a old high end model selling for cheap)
Derailleurs: best ones I can find for the price since apparently a 9 speed rear will work just fine (as long as my shifter is 7 speed).
New 7 speed cassette
New chainrings. This is the only item I have no clue on compatibility wise, especially when it comes to my current crank (is the mounting, etc standard?).

I'm currently in a bid for a set of used XT derailleurs and LX shifters for $30. The rest of the parts should be another $50 so I'm looking at maybe $100.

The sprockets have visible damage to them, so I think it's time they're replaced, and the left shifter has a bad spring, so it too needs to be replaced. The chain is too short (apparently it was changed some years ago). And I was told the derailleurs are at the end of their life, so I might as well change the derailleurs for a nicer model as it's not going to add too much to the total cost. Just putting my train of thought out there...